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43
Subgraph Isomorphism in Planar Graphs and Related Problems
, 1999
"... We solve the subgraph isomorphism problem in planar graphs in linear time, for any pattern of constant size. Our results are based on a technique of partitioning the planar graph into pieces of small treewidth, and applying dynamic programming within each piece. The same methods can be used to ..."
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Cited by 113 (1 self)
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We solve the subgraph isomorphism problem in planar graphs in linear time, for any pattern of constant size. Our results are based on a technique of partitioning the planar graph into pieces of small treewidth, and applying dynamic programming within each piece. The same methods can be used to solve other planar graph problems including connectivity, diameter, girth, induced subgraph isomorphism, and shortest paths.
Bicriteria network design problems
 In Proc. 22nd Int. Colloquium on Automata, Languages and Programming
, 1995
"... We study a general class of bicriteria network design problems. A generic problem in this class is as follows: Given an undirected graph and two minimization objectives (under different cost functions), with a budget specified on the first, find a ¡subgraph from a given subgraphclass that minimizes ..."
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Cited by 76 (13 self)
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We study a general class of bicriteria network design problems. A generic problem in this class is as follows: Given an undirected graph and two minimization objectives (under different cost functions), with a budget specified on the first, find a ¡subgraph from a given subgraphclass that minimizes the second objective subject to the budget on the first. We consider three different criteria the total edge cost, the diameter and the maximum degree of the network. Here, we present the first polynomialtime approximation algorithms for a large class of bicriteria network design problems for the above mentioned criteria. The following general types of results are presented. First, we develop a framework for bicriteria problems and their approximations. Second, when the two criteria are the same we present a “black box ” parametric search technique. This black box takes in as input an (approximation) algorithm for the unicriterion situation and generates an approximation algorithm for the bicriteria case with only a constant factor loss in the performance guarantee. Third, when the two criteria are the diameter and the total edge costs we use a clusterbased approach to devise a approximation algorithms — the solutions output violate
Algorithms For Vertex Partitioning Problems On Partial kTrees
, 1997
"... In this paper, we consider a large class of vertex partitioning problems and apply to those the theory of algorithm design for problems restricted to partial ktrees. We carefully describe the details of algorithms and analyze their complexity in an attempt to make the algorithms feasible as solutio ..."
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Cited by 40 (3 self)
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In this paper, we consider a large class of vertex partitioning problems and apply to those the theory of algorithm design for problems restricted to partial ktrees. We carefully describe the details of algorithms and analyze their complexity in an attempt to make the algorithms feasible as solutions for practical applications.
kNLC Graphs and Polynomial Algorithms
"... We introduce the class of knode label controlled (kNLC) graphs and the class of kNLC trees. Each kNLC graph is an undirected treestructured graph, where k is a positive integer. The class of kNLC trees is a proper subset of the class of kNLC graphs. Both classes include many interesting gr ..."
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Cited by 33 (2 self)
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We introduce the class of knode label controlled (kNLC) graphs and the class of kNLC trees. Each kNLC graph is an undirected treestructured graph, where k is a positive integer. The class of kNLC trees is a proper subset of the class of kNLC graphs. Both classes include many interesting graph families. For instance, each partial ktree is a (2 k+1 1)NLC tree and each cograph is a 1NLC graph. Furthermore, we introduce a very general method for the design of polynomial algorithms for NPcomplete graph problems, where the input graphs are restricted to treestructured graphs. We exemplify our method with the simple maxcut problem and the Hamiltonian circuit property on kNLC graphs.
Width parameters beyond treewidth and their applications
 Computer Journal
, 2007
"... Besides the very successful concept of treewidth (see [Bodlaender, H. and Koster, A. (2007) Combinatorial optimisation on graphs of bounded treewidth. These are special issues on Parameterized Complexity]), many concepts and parameters measuring the similarity or dissimilarity of structures compare ..."
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Cited by 19 (0 self)
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Besides the very successful concept of treewidth (see [Bodlaender, H. and Koster, A. (2007) Combinatorial optimisation on graphs of bounded treewidth. These are special issues on Parameterized Complexity]), many concepts and parameters measuring the similarity or dissimilarity of structures compared to trees have been born and studied over the past years. These concepts and parameters have proved to be useful tools in many applications, especially in the design of efficient algorithms. Our presented novel look at the contemporary developments of these ‘width ’ parameters in combinatorial structures delivers—besides traditional treewidth and derived dynamic programming schemes—also a number of other useful parameters like branchwidth, rankwidth (cliquewidth) or hypertreewidth. In this contribution, we demonstrate how ‘width ’ parameters of graphs and generalized structures (such as matroids or hypergraphs), can be used to improve the design of parameterized algorithms and the structural analysis in other applications on an abstract level.
Formallanguageconstrained path problems
 SIAM Journal on Computing
, 2000
"... Abstract. Given an alphabet Σ, a (directed) graph G whose edges are weighted and Σlabeled, and a formal language L ⊆ Σ ∗ , the formallanguageconstrained shortest/simple path problem consists of finding a shortest (simple) path p in G complying with the additional constraint that l(p) ∈ L. Here l ..."
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Cited by 19 (0 self)
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Abstract. Given an alphabet Σ, a (directed) graph G whose edges are weighted and Σlabeled, and a formal language L ⊆ Σ ∗ , the formallanguageconstrained shortest/simple path problem consists of finding a shortest (simple) path p in G complying with the additional constraint that l(p) ∈ L. Here l(p) denotes the unique word obtained by concatenating the Σlabels of the edges along the path p. The main contributions of this paper include the following: (1) We show that the formallanguageconstrained shortest path problem is solvable efficiently in polynomial time when L is restricted to be a contextfree language (CFL). When L is specified as a regular language we provide algorithms with improved space and time bounds. (2) In contrast, we show that the problem of finding a simple path between a source and a given destination is NPhard, even when L is restricted to fixed simple regular languages and to very simple classes of graphs (e.g., complete grids). (3) For the class of treewidthbounded graphs, we show that (i) the problem of finding a regularlanguageconstrained simple path between source and destination is solvable in polynomial time and (ii) the extension to finding CFLconstrained simple paths is NPcomplete.
Formal Language Constrained Path Problems
, 1998
"... Given an alphabet Sigma, a (directed) graph G whose edges are weighted and Sigmalabeled, and a formal language L , the Formal Language Constrained Shortest/Simple Path problem consists of finding a shortest (simple) path p in G complying with the additional constraint that l(p) 2 L. Here l(p) denot ..."
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Cited by 17 (9 self)
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Given an alphabet Sigma, a (directed) graph G whose edges are weighted and Sigmalabeled, and a formal language L , the Formal Language Constrained Shortest/Simple Path problem consists of finding a shortest (simple) path p in G complying with the additional constraint that l(p) 2 L. Here l(p) denotes the unique word given by concatenating the Sigmalabels of the edges along the path p. The main contributions of this paper include the following: 1. We show that the formal language constrained shortest path problem is solvable efficiently in polynomial time when L is restricted to be a context free language. When L is specified as a regular language we provide algorithms with improved space and time bounds...
Parallel Recognition of SeriesParallel Graphs
, 1992
"... Recently, He and Yesha gave an algorithm for recognizing directed series parallel graphs, in time O(log 2 n) with linearly many EREW processors. We give a new algorithm for this problem, based on a structural characterization of series parallel graphs in terms of their ear decompositions. Our ..."
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Cited by 15 (1 self)
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Recently, He and Yesha gave an algorithm for recognizing directed series parallel graphs, in time O(log 2 n) with linearly many EREW processors. We give a new algorithm for this problem, based on a structural characterization of series parallel graphs in terms of their ear decompositions. Our algorithm can recognize undirected as well as directed series parallel graphs. It can be implemented in the CRCW model of parallel computation to take time O(log n). In the EREW model the time is O(log 2 n) but the number of processors required improves the bounds of the previous algorithm. 1 Introduction A directed graph G is twoterminal series parallel, with terminals s and t, if it can be produced by a sequence of the following operations: 1. Create a new graph, consisting of a single edge directed from s to t. 2. Given two twoterminal series parallel graphs X and Y , with terminals s X , t X , s Y , and t Y , form a new graph G = P (X,Y ) by identifying s = s X = s Y and t = ...
Optimal reduction of twoterminal directed acyclic graphs
 SIAM Journal on Computing
, 1992
"... Abstract. Algorithms for seriesparallel graphs can be extended to arbitrary twoterminal dags if node reductions are used along with series and parallel reductions. A node reduction contracts a vertex with unit indegree (outdegree) into its sole incoming (outgoing) neighbor. This paper gives an O ..."
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Cited by 14 (1 self)
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Abstract. Algorithms for seriesparallel graphs can be extended to arbitrary twoterminal dags if node reductions are used along with series and parallel reductions. A node reduction contracts a vertex with unit indegree (outdegree) into its sole incoming (outgoing) neighbor. This paper gives an O(n2"5) algorithm for minimizing node reductions, based on vertex cover in a transitive auxiliary graph. Applications include the analysis of PERT networks, dynamic programming approaches to network problems, and network reliability. For NPhard problems one can obtain algorithms that are exponential only in the minimum number of node reductions rather than the number of vertices. This gives improvements if the underlying graph is nearly seriesparallel.